Hollow bodies capable of being produced by folding sheet material



June 11, 1940; P, KEL 2,203,697

HOLLOW BODIES CAPABLE OF BEING PRODUCED BY FOLDING SHEET MATERIAL Filed Sept; 2,1937 2 Sheets-Sheet 1 ,QTTOIENEYS P. RINKEL 2,203,697

ING SHEET MATERIAL June 11, 1940.

HOLLOW BODIES CAPABLE OF BEING PRODUCED BY FOLD Filed Sept. 2, 1937 2 Sheets-Sheet 2 ,NVENTdR Y PAWL Pwvmsz. wg; IQTTGRNEYS Fig. 77

Patented June 11, 1940 HOLLOW BODIES UA'PABLEI OF BEING LYPRO DUOEDQBY: EOLDING SHEET MATERIAL Pauli Rink'el," nerlimoharlottenbura. Germany,

assign'or" to Hans Weillfi New York Applicatiomseptembert2, 1937",- Serial No; 162,1061

In.--Germany Eebruary ;.19373' plane-and;therefore:canibemrodilcedfrom aizpl'ane sheet without the "necessity: of cuttingtoutiparts i or adding parts thereto onproducing:partszfoldedi I I back uponitself. v

The cpresent invention ism, not-l concernedxwithc I these 1 simple} :bodies but; with; gnore complicatedc bodies the surroiinding surfaces,ofi which lMWOllldJi not: be expected to ebecproduceda alsoobya'ieldingit 2m sheet I material: without 1 themnecessityvofircuttifng't out; parts i or adding 1.parts=1-theretoi;oraproducinge parts folded p back guponn itself.; Th invention; however, shows how it;isvpossibleetorafind 4811011?! peculiar bodies: and. to produce themepracticallym 5- provided that certain rules are follbwedw.

A glance eat the I drawingsawhich show several embodiments of the iinvention JGVSSJSnh-OW weny' varied and sunprisingare the-bodiesacconding.to z the I invention although ltheasurroundingesurfaces ;;thereof are-in: fact evolvabler. I i

For reasons whichi will1bewexplainedhereinafter the bodies; according to thevinvention; have? two z characteristic f eatures: namely: that at" tleastv in a one partial zone of the total heightrthereofaexiste 5 edges which have no common-plane. and ,alsmthat the-surfaces enclosing the'uti-lisable innemspacce comprise inwardly directed partsw The expression partiabzonemeans apart Oil the surrounding;surfaces-(of 'a ibody containedi- I between two sectional planes v-lpanallelmtoeeache other and to the base OIlnWhiCh theibodyifwmayx stand, the distance: between the isaid rsectionahq planes being a fraction yof the total; height? Dfuthfi body.

Inwandly 1vdirected parts mayabexdennediby thee condition that the straight dine-eonneetingetwor points thereonfallaoutside the body It is to be understood that the tinventiom-alsow consists in the :vanious mattersdescribedahereine I afterandlclaimed. I

The invention will; be: ibetter: 1 understoodcfromi 1 the following; description I 1731136111111: ,conjunctionl'i with the -accompanying adrawinge, in Nam ousi embodiments, of, the :inventiom aremshowni bye way of example. I

Figs: lashowsga partializon'ei otia-xhmlow body evolved; into .a plane." I

Fig; Zirisrsthe: corresponding: plan" view of that a zone; l

, Fig: 31 is :the 'corresp-onding front; view; 5

Fig. 4 vista corner i'of such .a; zone drawmoma I greater scaler Figpbris aafront view ofsa partial zone'of greater heigh nandis'di'fferent formi.

Fig 6*.shows a part :of the surface =of that'zone 10 evolvedirintoaa:plane:

Fig. 7 is theiront view'oftanotherzonee I Fig; 8 ie againia part of thei'surfaceiof that 'zone evolved :into a? planecii t I Fig 9 is aiplan ivi'ewl:offanother zoned Fig. 10 is a part of the sunfaceof thatizone' evolved into a plane.

Fig. 11 is a perspective view-ofa complete body.

Fig, 12 shows the total surface of that body evolved into aplane; I

Fig. 13*isthe plan-view, F-i'gel l is lwh'OTiZO'l'llidl cross-section in the middle and Fi 'gjl5'isa -per spective View of a further example of a body according to the inventiomt Fig 16 isthe surroundingisurface of that body evolved into a plane. I

Figs. 17, 18," 19; and-20 eareperspectiveviews respectivelyofi further embodiments of=the inven tion..

Figs. 1-10 are intended to-aid in explaining the relationships-to-be known: when surfacesaccording to tl' ie inventionv are to be constructed. Thea strip of sheet-material istprovided with-lines I,- 2,6,? .455 suchthatzwhen the strip is folded along-v the said lines anduthe u ends 6 andfi are made-to meet, l a I partialc lzone I is i produced and made to a stand up as shown in Figs. 2 and 3.

InFig; 1 as wellasrin alltheother-figures illustrating revolved: surfaces the foldmgdines :shown inful1(2, 3,= 5, 6;;6) tindicate edges which in the-aio completed bodyrare directed outwardly whilst the v broken lines indicate edgesdirected-inwardly (I and-A). I Outwardlyvdirectededgesare suchthat theinner angle of the adjacent surfaces is smallerl I than-180. I Inwardly directed edges-are such-thatdfi the \inneri angler between" theadjacent surfaces rise greater thandh Therefore the-edges indicated by ,broken lines in the involved -:surfaces -must be formed by ;-folding the *strip in the reverse direction to that which applies tothe full i lines. a

Referring to Fig. 4 a strip 8 of widthb is fo1ded' along ithe (oblique. I line I 9 ztoformham edgefi The upper edgeof the strip t8 is designated bw-I (hand 1 I0; whilstithe-lowers edge is de'signated byaltl and I I. I I and I I' have a commonplanewhich may r I negative'value of 2 (+2: and -z).

base plane H, H. said two limiting planes is designated by h and the projection plane.

be considered as the base on which the folded strip may stand. Since ll] is parallel to H, and It parallel to H, it follows that the plane containing the edges l and I0 which is the upper limit of the upstanding strip 8 is parallel to the The distance between the this is the height of the zone. The angle 'y between 19 and h indicates the inclination of the strip. Since the width of the strip is everywhere equal to b, and the zone height everywhere equal to h, the angle which the strip at every part makes with the vertical h isv constant, that is everywhere that angle must be equal to 7, but the strip on either side of a folded edge is inclined in opposite direction. This means that the angle 7 changes its sign from corner to corner; as shown in Fig. 2 which is a plan view it will be seen that the lower. limiting edge of the zone is offset with inclinations with the bisector. of the external angle ofthe corresponding corner of the polygon. In Fig. 4 I2 is the projection of the oblique folded edge 9 and also the bisector of the external angle 25 of the corner of the polygon shown..

Furthermore the following. mathematical relationship may be derived from Fig. 4: let a be the -.anble between the folded edge 9 and the strip edge H1 or II, then In passing around the zone '7 is alternately positive and negative; consequently sin 'y and therefore the ratio tan 6 tan a alternates between the positive value and the From this fact-rules such as the following may be derived for the construction of hollow bodies from sheet material according to the invention.

1-. Where the angles c follow each other without a change of sign, that is where only outwardly directed edges (or only inwardly directed edges) follow each other, the successive angles at alternate in signpthat means that in the evolved surfacesthe successive folding edges are inclined alternately outwards and inwards, seefor instance 2 and 3 in Fig. 1.

'2. Where, however, the angles ,6 alternate in sign, the successive angles a have like signs; that means that inthese cases, in the evolved sur faces, the successive folding edges are inclined in the same'sense, see for instance 3, l, 5 in Fig. 1.

Subject to the above equation and to the above rules it is possible to elect arbitrarily a basic *polygon and to calculate and design the evolved form of corresponding surfaces and so the hollow bodies of the kind mentioned, that is to define the necessary location of the folding lines on the sheet material and also to indicate which ofthe in the-other sense. 7

It will be understood that groups of particular folds are to be made in one direction and which forms will require additional rules special for that group as will be pointed out in connection with the respective examples;

Just as above hollow bodies of the kind referred to are considered as being divisible into partial one which is identical with the zone shown in .Figs. 1, 2 and 3 having folded edges [-6. The l strip 1 corresponds to the strip l9, and the edges |G correspond to the edges 13-! 8. Fig. 6 which shows a part of the evolved surface of the body shown in Fig. 5 contains in theline of contact of the partial strips 1 and 19 (plane of contact of the partial zones) further folding edges 20, 2|, 22, 23 which arealso directed alternately outwardly and inwardly.

Since it is possible to choose at will, as indicated above, any value of 'y varying from zone to zone, so it is also possible to provide for a gradual change of the angle of inclination in the Vertical direction. Thus curved side surfaces may be obtained, audit is surprising that in this manner curved folded edges are obtained which in each differential of the height thereof follow the rules indicated above.

An example is shown in Figs. 7 and18. By .fi

comparing Figs. 5and '7 it will be seen that the crooked line formed by the continuous edges for instance I and I3, or 2 and I4 are replaced by the curved lines or edges 24 and 25 respectively; furthermore it will be seen that the outwardly directed edge 20 corresponds to the convex surface lying between the curved edges 28 and 24, whilst the inwardly directed edge 2! corresponds to the concave surface lying between the curved edges 24 and 25, and so on. i

It is to be noted that the plan View shown in Fig. 2 is not only that of the body illustrated in Fig. 3 but also of those shown in Figs. 5 and '7.

In order to'facilitate the reading of the drawings and to show better the direction in space of the different parts of the surfaces in the figures just mentioned as well as in the figures which follow, the overhanging. outwardly directed surfaces are shaded.

Figs. 9 and show in a similar manner a body composed of three partial zones the uppermost of which is identical with that shown in Figs. 1-3 and is therefore provided with the same designations; On to this first zone or strip 7 is juxtaposed a second strip 29 with smaller inclinationbut in the same sense, and on to this second strip is juxtaposed a third strip 30 havingvertical walls, that is a prism. As shown by Fig. 9, the continuous edges theparts of which have different inclinations lie in a'vertical plane including the said parts.

The elementary examples described with reference to Figs. 1-10-Sh0W clearly the existence of two-characteristic features common to them all. The outer surfaces surrounding the utilisable inner space comprise inwardly directed parts, and furthermore in all these cases exist edges having no common plane. Thus-these features are characteristic of the bodies formed according to the invention.

The following figures illustrate practicalembodiments of the invention.

Fig. 11 shows a body which is apolyhedron in which two outwardly directed edges 32 arefollowed in regular sequence .by one inwardly directed edge 3| By. the middle section shown in'Fig. ll the inwardly directed parts are made clear; Fig. 12 shows not only the evolved surfaces but also the form of a blank from which the complete body is formed including the neceshow the idea of the invention may be embodied in the surroundingsurface of a single frustum of a body. In this case in the surrounding surface an outwardly directed edge 35 alternates with an inwardly directed edge 36, as also in:

dicated in Fig. 16 whichis the evolved surface.

This is also clear from an inspection of Fig. 13 which is a plan view and Fig. 14 which is a middle cross section. I

In both examples the inwardly. directed edges have a different inclination to the outwardly directed edges. The outwardly directed edges lying on each side of an inwardly directed edge are such that they have no common. plane.

lEhe following example shows an embodiment in which the surrounding surfaces of the hollow bodies are formed by superimposing the sur rounding surfaces of aplurality of frusta of bodies. Y

The example according to Fig. 17 is obtained by superimposing two bodies as shown in Fig. 11

and a six-sided prism. Thetwo first-mentioned bodies are superimposed after being turned through with respect to eachother, results in the peculiarityas shown in Fig. 17 that in the imaginary plane of contact only two outwardly directed edges 31 are obtained, whilst some of the meeting partial surfaces of the upper and the lower frusta are continuous one of the other thereby forming no edge, since they possess identical inclinations. In thepolygon of contact between the described part of the body and the lowest prismatic part only two inwardly directed edges 38 are obtained, whilst all the remaining edges 39 are outwardly directed. p

A further example of this peculiarity is shown in Fig. 20, which il'lustratesa hollow body of similar type as Fig. 15. The outwardly directed edges. 59 correspondto the edges 35 of Fig. 15; the inwardly directed edges that would correspond-to the edges 35 are absent. They are again replaced by inwardly directed curvatures of each of the partial surfaces formed automatically between two adjacent outwardly directed edges 59. Fig. 18 shows a body the edges 49 and 50 of which are in sequence around the surface directed alternately outwardly and inwardly, exactly as shown in the example o f Fig. 15. Fig. 19 shows a hollow body in which the upper half is identical with the upper half of the body shown in Fig. 18, but. the lower half of which is This ' A body according to. Fig. '18 possesses still an other remarkable technical function. If the body is made of resilient material and if the internal pressure is greater than the external pressure, the body has a tendency to extend and at the same time its ends turn in opposite direction with respect to each other. Thus such a body may be used as a pressure gauge.

The final shape of a hollow body can be predetermined by p-rovidinga piece of sheet material with continuous lineswhichare arranged in such a. manner that after thesheet is folded along: the I said linesandbent to bring the ends together a hollow body results having edges coinciding with the said lines. It is of secondary importance whether the said lines are actually drawn or effected in any optical manner, or whether they are produced mechanically such as formingthat a finished body is used as a mandrel; the said body having a shape corresponding to a hol low body according to the invention so that when.

a. sheet material is simply wrapped around the said body it automatically takes up the same form. The said body which is to be wrapped may be firstly a hollow body for instance a folded box whichis constructed and. produced according to the invention and is to be provided subsequently with a further wrapping for instance transparent paper; secondly the said body may be the article itself which is to be packed or wrapped;

finally it may be. a framework the members 01" which correspond to the edges of the desired shape, whilst the surrounding surfaces are obtained by wrapping. a

I wish it tobe understoodthat I do not desire to be limited to exact details of construction shown and described, for obvious modifications will occur to a person skilled in the art.

What-I claim is: p

l. A hollow body capable of being produced byfolding sheet material and comprising-- side walls; the developmentof said side walls constituting a strip with straight-lined and unbrokon upper and lower edges parallelto each other,

said body including at least one partial zone of its entire height, defined by two parallel CI'OSS".

sectional planes, said partial zone comprising other edges extending from one of said planes to the other and lateral partial surfaces between said other edges respectively, at least two of said other edges having no plane common with eachother, and at least one portion of one of the circumferences ofsaid planes being inwardly protruding.

2. A hollow body as claimed in claim 1 in which said partial surfaces and other edges are arranged in a cyclic-ally repeated sequence around the circumference of said partial zone.

3. A hollow body capable of being produced by folding sheet material and comprising side Walls, the development of said side walls constituting a strip with straight-lined and unbroken upper and lower edges parallel to each other, said body including at least one partial zone of its entire height, defined by two parallel crosssectional planes, said partial zone comprising at least one set of other edges extending from. one of said planes to the other and lateral partial surfaces, at least two of said other edges having no plane in common with each other, at least one portion of one of the circumferences of said planes being inwardly protruding, andthe development of said :zone forming. a' parallelogram inwh'ich the: circumferences of said planes constitutethe one pair of parallel sides, and in which, said other edges are parallel to the other pair of parallel sides. i

4. A hollow body capable of being produced by folding sheetmaterial and comprising parallel top and bottom planes, side walls and two sets of lateral edges, none of said edges having a plane in common with one of the other edges .of the same-set, .said body including partial zones of its entireheight, defined by two parallel cross-sec- Iii tional planes,.at least one of the circumferences of each of said cross-sectional planes having inwardlynand outwardly protruding corners, and the development: of the side walls of said body forming a. parallelogram, in which the circumferences of said top and bottom planes constitute the one pair of parallel sides, and in which one set .of said edges are parallel to the other pair of parallel sides, so as to. divide said parallelogram in a plurality of partial parallelograms, the other set of edges defining, said inwardly protruding corners, being coincident with the longer diagonals'of said partial parallelograms.

5. A hollow body capable of being produced by folding sheet material and comprising side walls,

' one of said planes to the other, and lateral partial surfaces between said curved edges respectively, the curvatures of all said curved edges having like sense, none of said curved edges having a plane in common with another one, at least one of the circumferences of said planes having portions alternately protruding inward and outward, and the development of said zone forming a strip with straight-lined and unbroken upper and lower edges parallel to each other.

6. A hollow body as claimed in claim 5 in which said curved edges alternately protrude inwardly and outwardly, eachsurfaceportion between the concave side of an outwardly protruding edge and the convex-side of an inwardly protruding edge being concave, and each surface portion between the convex side of an outwardly protruding edge and the concave side of an inwardly protruding edge being convex.

7. A hollow body as claimed in claim 5 made of resilient material for use as a pressure gauge.

8. A container capable of being produced by folding sheet material and comprising side walls,

the development of said side walls constituting a strip with straight-linediand unbroken upper'and lower edges parallel to each other, said container including at least two bodies superimposed one on the other, the tops and the bottoms of said bodies being arranged parallel to each other, and the top circumference of the lower body being identical with the bottom circumference of the upper body, at least one of said bodies including at least: one partial zone of its entire height, defined by two parallel cross-sectional planes, said partialzone comprising other edges extending from one of said planes to the other and lateral partial surfaces between said other edges respectively, at least two of said other edges having no truding edges, the development of said side walls Y constituting a parallelogram, said parallelogram being subdivided by said outwardly protruding edges in a plurality of triangles having their bases alternately on the upper and lower sides respectively of said parallelogram, and partial paral-v lelograms between said triangles, said inwardly protruding edges being coincident with the longer diagonals of said partial parallelograms.

10. A container capable of being produced by folding sheet material and comprising side walls, the development of said side walls constituting a strip with straight-lined and unbroken upper and lower edges parallel to each other, said container including at leasttwo bodies superimposed one on the other, the tops and the bottoms of said bodies being arranged parallel to each other, and the top circumference of the lower body being identical with thebottomcircumference of the upper body, each of said two bodies including at least one partial zone of its entire height, defined by two parallel crossfsectional planes, said par,- tial zone comprising other edges extending from one of said planes to the other and lateral partial surfaces between said other edges respective- 1y, at least two of said other edges having no plane in common with each other, and at least one portion of one of the circumferences of said planes being inwardly protruding, at least one of 

